PRACTICAL APPLICATIONS OF POSTERIOR PREDICTIVE MODEL CHECKING FOR ASSESSING FIT OF COMMON ITEM RESPONSE THEORY MODELS

Some issues on posterior predictive model checks for item response theory models ∗

Assessing the validity of model assumptions is a crucial part of any parametric statistical analysis. The question of interest is whether a particular specified model appears to provide an adequate fit. For item response theory models the goodness-of-fit problem has not been completely solved. The possible number of response patterns is large for even moderately long assessments, leading to spa...

Goodness-of-Fit Assessment of Item Response Theory Models

The article provides an overview of goodness-of-fit assessment methods for item response theory (IRT) models. It is now possible to obtain accurate p-values of the overall fit of the model if bivariate information statistics are used. Several alternative approaches are described. As the validity of inferences drawn on the fitted model depends on the magnitude of the misfit, if the model is reje...

A Bayesian Nonparametric Model Fit statistic of Item Response Models

GOF OF IRT MODELS 1 Goodness of fit assessment of item response theory models

The article provides an overview of goodness of fit assessment methods for item response theory (IRT) models. It is now possible to obtain accurate p-values of the overall fit of the model if bivariate information statistics are used. Several alternative approaches are described. As the validity of inferences drawn on the fitted model depends on the magnitude of the misfit, if the model is reje...

Limited-information goodness-of-fit testing of item response theory models for sparse 2 tables.

Bartholomew and Leung proposed a limited-information goodness-of-fit test statistic (Y) for models fitted to sparse 2(P ) contingency tables. The null distribution of Y was approximated using a chi-squared distribution by matching moments. The moments were derived under the assumption that the model parameters were known in advance and it was conjectured that the approximation would also be app...